Equilibrium. Stable equilibrium (negative feedback)

Equilibrium

Equilibrium

Stable equilibrium (negative feedback)

Unstable equilibrium (positive feedback)

• ,

At Equilibrium:Inflows=Outflows

At Equilibrium:Inflows=Outflows

80 gal/min120 gal ???

Assume Equilibrium:Inflows=Outflows

80 gal/min120 gal 80 gal/min

At Equilibrium:Inflows=Outflows

80 gal/min120 gal 20 gal/min

Is water levela) rising b) Fallingc) Staying the same

At Equilibrium:Inflows=Outflows

80 gal/min120 gal 20 gal/min

Is water levela) rising b) Fallingc) Staying the same

At Equilibrium:Inflows=Outflows

80 gal/min120 gal 80 gal/min

Is water levela) rising b) Fallingc) Staying the same

At Equilibrium:Inflows=Outflows

80 gal/min120 gal 80 gal/min

Is water levela) rising b) Fallingc) Staying the same

At Equilibrium:Inflows=Outflows

80 gal/min120 gal 140 gal/min

Is water levela) rising b) Fallingc) Staying the same

At Equilibrium:Inflows=Outflows

80 gal/min120 gal 140 gal/min

Is water levela) rising b) Fallingc) Staying the same

At Equilibrium:Inflows=Outflows

Is water levela) rising b) Fallingc) Staying the same

=2 min

8 gal/min 20 gal??=_________

At Equilibrium:Inflows=Outflows

Is water levela) rising b) Fallingc) Staying the same

=2 min

8 gal/min 20 gal??=_10 gal/min________

At Equilibrium:Inflows=Outflows

Is water levela) rising b) Fallingc) Staying the same

=2 min

8 gal/min 16 gal??=_________

At Equilibrium:Inflows=Outflows

Is water levela) rising b) Fallingc) Staying the same

=2 min

8 gal/min 16 gal??=__8 gal/min_______

At Equilibrium:Inflows=Outflows

Is water levela) rising b) Fallingc) Staying the same

=2 min

8 gal/min 12 gal??=_________

At Equilibrium:Inflows=Outflows

Is water levela) rising b) Fallingc) Staying the same

=2 min

8 gal/min 12 gal??=___6 gal/min_____

At Equilibrium:Inflows=Outflows

Is pollutant levela) rising b) Fallingc) Staying the same

8 ppm/yr12 ppm

=.2 (1/yr)

??=_________

At Equilibrium:Inflows=Outflows

Is pollutant levela) rising b) Fallingc) Staying the same

8 ppm/yr12 ppm

=.2 (1/yr)

??=__2.4 ppm/yr____

At Equilibrium:Inflows=Outflows

Is pollutant levela) rising b) Fallingc) Staying the same

8 ppm/yr??

=.2 (1/yr)

8 ppm/yr

What is the lifetime?

At Equilibrium:Inflows=Outflows

Is pollutant levela) rising b) Fallingc) Staying the same

8 ppm/yr??= 40 ppm

=.2 (1/yr)

8 ppm/yr

What is the lifetime?Lifetime=1/(DecayConstant)=5 yr

Whenever the

net flow = -k*stock you get exponential decay to zero**

Summary (exponential decay/Goal seeking)

kteXX 0

Sometimes we like to use the concept of lifetime (decay time constant) instead of decay rate constant.

Here k is the decay rate constant.

k

1

kXdt

dXas wrtten be wouldmath thisin **

Whenever the

net flow = inflow-k*stock you get exponential decay to a Goal, Xeq

Summary (exponential decay/Goal seeking)

eqkt

eq XeXXX 0

The Goal is the value of X (the stock) that makes the net flow zero

Inflow=outflow

Inflow=k*stock at equilibrium

Here X is any stock.

*inf

*inf

lowX

or

XXklow

eq

eqeq

Ceq=Inflow*lifetime

Ceq=Inflow/(DecayRateConstant)

Outflow=Content/(lifetime)

Outflow=DecayRateConstant*Content

Summary (exponential decay/Goal seeking)